The magnetic coils of a tokamak fusion reactor are in the shape of a toroid having an inner radius of 0.700 m and an outer radius of 1.20 m. The toroid has 900 turns of large diameter wire, each of which carries a current of 13.0 kA. Find the difference in magnitudes of the magnetic fields of the toroid along the inner and outer radii. (Enter your answer in T.)
Answer:
The difference is [tex]\Delta B = 1.39 \ T[/tex]
Explanation:
From the question we are told that
The inner radius is [tex]r_i = 0.700 \ m[/tex]
The outer radius is [tex]r_o = 1.20 \ m[/tex]
The number of turns is [tex]N = 900 \ turns[/tex]
The current on each wire is [tex]I = 13.0 kA = 13*10^{3} \ A[/tex]
Generally magnetic field of a toroid along the outer radius is mathematically evaluated as
[tex]B_o = \frac{\mu_o * N * I}{2 \pi r_o}[/tex]
Where [tex]\mu_o[/tex] is the permeability of free space with value [tex]\mu_o= 4\pi * 10^{-7} N/A^2[/tex]
substituting values
[tex]B_o = \frac{ 4\pi * 10^{-7} * 13*10^{3} * 900}{ 2 * 3.142 * 1.20}[/tex]
[tex]B_o = 1.95 \ T[/tex]
Generally magnetic field of a toroid along the inner radius is mathematically evaluated as
[tex]B_i = \frac{\mu_o * N * I}{2 \pi r_i}[/tex]
substituting values
[tex]B_i = \frac{ 4\pi * 10^{-7} * 900 * 13*10^{3}}{2 *3.142 *0.700}[/tex]
[tex]B_i = 3.34 \ T[/tex]
The difference in magnitudes of the magnetic fields of the toroid along the inner and outer radii is mathematically evaluated as
[tex]\Delta B = B_i – B_o[/tex]
[tex]\Delta B = 3.34 -1.95[/tex]
[tex]\Delta B = 1.39 \ T[/tex]